So you used priming sugar instead of Co2? sure, it'll carb up and 'age/mellow' while carbing. But you can't put it in the fridge yet! Doing so will put the yeast to sleep and it won't carb.
side note: Just so we're using the same terminology, force carbing is using Co2 to carbonate. you can do this by 'set it and forget it' method of putting it at serving pressure (12psi or so) for 10 days. or, you can RAPID force carb by putting it at 30psi and rocking the keg several times for a few hours.
many new keggers think force carbing has to be done rapidly, so I wanted to make sure you had all your options available.
I don't prime kegs with sugar because its that much more yeast cake being created in the keg I have to remove before I an pour a good clean beer.